With regard to an engine brake running mode performed with engine brake applied by driven rotation of an engine while the engine and wheels are kept connected, an inertia running mode is conceived that is performed with an engine brake force reduced by separating the engine from the wheels by a connecting/disconnecting device for extending a running distance and improving fuel consumption. A device described in Patent Document 1 is an example thereof and, two types of the inertia running mode are proposed as (a) a neutral inertia running mode performed with the engine separated from the wheels by a clutch (the connecting/disconnecting device) while the engine is supplied with fuel and allowed to perform self-sustaining rotation, and (b) a free-run inertia running mode performed with the engine separated from the wheels by the clutch while the fuel supply to the engine is stopped to stop the rotation. Either of these types of the inertia running modes is performed under a certain condition without particular distinction.